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Macaulay2Doc :: fine control of a Groebner basis computation

fine control of a Groebner basis computation

Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.

Partially computed Groebner bases

Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
i2 : I = ideal(random(3,R),random(3,R),random(3,R))

                  3        2            2         3        2                
o2 = ideal (13181a  - 6796a b - 15163a*b  + 12864b  - 6301a c + 11815a*b*c +
     ------------------------------------------------------------------------
          2           2           2        3        2                      2 
     3855b c + 1655a*c  + 11641b*c  - 1590c  + 2179a d + 1330a*b*d - 10627b d
     ------------------------------------------------------------------------
                                     2           2          2          2  
     + 3257a*c*d + 3201b*c*d + 11892c d - 7655a*d  - 7175b*d  + 8984c*d  +
     ------------------------------------------------------------------------
          3        2                     2                            
     1348d  + 9532a e - 7459a*b*e + 5383b e - 12087a*c*e - 3503b*c*e -
     ------------------------------------------------------------------------
          2                                               2           2  
     3462c e - 12267a*d*e + 1559b*d*e + 5038c*d*e - 11977d e + 3871a*e  +
     ------------------------------------------------------------------------
            2          2           2        3          3        2           2
     5256b*e  + 3666c*e  - 14641d*e  + 9071e , - 12560a  - 9905a b + 6716a*b 
     ------------------------------------------------------------------------
             3        2                     2            2           2  
     + 14194b  + 1905a c + 1940a*b*c + 5800b c - 11061a*c  + 15147b*c  -
     ------------------------------------------------------------------------
           3         2                       2                            
     12957c  + 11056a d + 14702a*b*d + 13113b d + 2056a*c*d + 12647b*c*d -
     ------------------------------------------------------------------------
           2            2          2           2         3        2   
     14276c d - 10216a*d  + 5817b*d  - 11667c*d  - 10894d  + 1389a e +
     ------------------------------------------------------------------------
                       2                                  2                
     2756a*b*e - 15393b e - 7812a*c*e - 10719b*c*e + 2976c e + 13997a*d*e -
     ------------------------------------------------------------------------
                                   2           2          2           2  
     1566b*d*e + 12103c*d*e + 5821d e + 2265a*e  - 6401b*e  + 14600c*e  -
     ------------------------------------------------------------------------
            2        3       3        2            2         3         2   
     8076d*e  + 3162e , 1015a  + 4428a b + 14671a*b  + 14136b  - 10599a c -
     ------------------------------------------------------------------------
                      2           2         2        3        2              
     3243a*b*c - 8711b c - 2546a*c  - 888b*c  + 2004c  + 4865a d - 15126a*b*d
     ------------------------------------------------------------------------
            2                                  2           2          2  
     + 2787b d + 9811a*c*d + 11685b*c*d - 8273c d + 7518a*d  + 7898b*d  -
     ------------------------------------------------------------------------
             2        3        2                    2               
     12023c*d  - 7857d  + 6922a e - 3277a*b*e - 284b e - 6385a*c*e +
     ------------------------------------------------------------------------
                        2                                             2   
     13359b*c*e + 11526c e + 344a*d*e + 2773b*d*e + 13551c*d*e - 9439d e +
     ------------------------------------------------------------------------
             2          2          2          2         3
     10817a*e  + 4070b*e  + 5853c*e  + 1551d*e  + 12626e )

o2 : Ideal of R
i3 : gens gb(I,PairLimit=>7);

             1       7
o3 : Matrix R  <--- R
Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
i5 : leadTerm gens g

o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o5 : Matrix R  <--- R
We can make a Groebner basis snapshot by using StopBeforeComputation, or gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)

o6 = | ab2+11230b3+5619a2c-9642abc-1486b2c-6177ac2+15422bc2-11641c3+12588a2d+
     ------------------------------------------------------------------------
     7875abd-6830b2d+4507acd+12549bcd-15903c2d+1573ad2+13402bd2-13295cd2+
     ------------------------------------------------------------------------
     15589d3-8422a2e+15204abe-1341b2e-12355ace-14904bce+15510c2e+15844ade+
     ------------------------------------------------------------------------
     4806bde+10382cde-12087d2e+8248ae2+14878be2+10256ce2-5957de2+14367e3
     ------------------------------------------------------------------------
     a2b+12964b3+12471a2c+15975abc+11156b2c-3375ac2-1361bc2-13556c3+5782a2d+
     ------------------------------------------------------------------------
     14672abd-6086b2d+9182acd+12715bcd-200c2d+5343ad2-8055bd2-10824cd2+
     ------------------------------------------------------------------------
     11248d3+11070a2e+570abe-14988b2e+8286ace+5524bce+5281c2e-14161ade-
     ------------------------------------------------------------------------
     2076bde+5911cde-7686d2e-12453ae2+6293be2-6040ce2+1577de2-14623e3
     ------------------------------------------------------------------------
     a3-5499b3+2373a2c-4991abc+15714b2c+13608ac2-3549bc2-10839c3-11115a2d-
     ------------------------------------------------------------------------
     11402abd+1047b2d+7496acd-4373bcd+6393c2d-10157ad2+9110bd2+15419cd2-
     ------------------------------------------------------------------------
     13493d3-14617a2e-4158abe-10042b2e-9201ace-11777bce+12249c2e-8196ade+
     ------------------------------------------------------------------------
     12427bde+4767cde-15382d2e-13991ae2-7474be2-9608ce2-11392de2-9413e3
     ------------------------------------------------------------------------
     b3c+1150a2c2-10131abc2-14549b2c2-12164ac3+13503bc3-12303c4-899b3d+
     ------------------------------------------------------------------------
     14272a2cd-5265abcd+11475b2cd-7043ac2d+569bc2d+14672c3d+14826a2d2+
     ------------------------------------------------------------------------
     10192abd2+6972b2d2-9254acd2-10634bcd2+12984c2d2+10607ad3+14637bd3+
     ------------------------------------------------------------------------
     7308cd3+14369d4-10952b3e-2459a2ce-12846abce-10003b2ce-10091ac2e+2597bc2e
     ------------------------------------------------------------------------
     +13536c3e-6760a2de-7364abde-4499b2de+556acde-7320bcde-980c2de-12093ad2e-
     ------------------------------------------------------------------------
     7289bd2e-12204cd2e+12265d3e+12910a2e2+5770abe2+5023b2e2-11068ace2+
     ------------------------------------------------------------------------
     8141bce2-2072c2e2-10678ade2-13592bde2+12499cde2+8365d2e2-9763ae3+
     ------------------------------------------------------------------------
     15062be3+2946ce3-9663de3-7485e4
     ------------------------------------------------------------------------
     b4+15838a2c2+11166abc2-9123b2c2-4742ac3+12361bc3-8216c4+4085b3d+
     ------------------------------------------------------------------------
     12070a2cd-15329abcd-11790b2cd-13025ac2d+928bc2d+472c3d+8944a2d2-8918abd2
     ------------------------------------------------------------------------
     +12046b2d2+15431acd2-1077bcd2-10532c2d2+4356ad3-4638bd3+3192cd3-12676d4-
     ------------------------------------------------------------------------
     13709b3e+14884a2ce+3111abce-1148b2ce+15455ac2e+7476bc2e-4397c3e-4565a2de
     ------------------------------------------------------------------------
     -1416abde+15400b2de-14278acde+7677bcde-6288c2de-12394ad2e-2672bd2e+
     ------------------------------------------------------------------------
     1762cd2e+7054d3e+1058a2e2+9056abe2+15492b2e2+10508ace2-11965bce2+
     ------------------------------------------------------------------------
     2223c2e2+12164ade2-13974bde2+5908cde2-12103d2e2+13428ae3-895be3+6469ce3+
     ------------------------------------------------------------------------
     11025de3-2370e4 abc3-9444b2c3-346ac4+5019bc4-13789c5-4402a2c2d-
     ------------------------------------------------------------------------
     14076abc2d-3149b2c2d+9884ac3d+14534bc3d+9973c4d-11971b3d2+1531a2cd2+
     ------------------------------------------------------------------------
     3200abcd2-12036b2cd2-4285ac2d2+3896bc2d2-6259c3d2+8847a2d3+1213abd3+
     ------------------------------------------------------------------------
     4751b2d3-12664acd3-9056bcd3+13230c2d3+1069ad4+5657bd4-7486cd4+6763d5+
     ------------------------------------------------------------------------
     14275a2c2e+13733abc2e+8449b2c2e+13476ac3e+15747bc3e-12660c4e-6616b3de+
     ------------------------------------------------------------------------
     11438a2cde-13504abcde-8366b2cde+15407ac2de+8366bc2de-7069c3de+7204a2d2e+
     ------------------------------------------------------------------------
     4025abd2e+7348b2d2e+7165acd2e-11181bcd2e-393c2d2e+2951ad3e+11806bd3e+
     ------------------------------------------------------------------------
     2702cd3e-1030d4e+9909b3e2+11140a2ce2+6786abce2-8122b2ce2-13603ac2e2+
     ------------------------------------------------------------------------
     4662bc2e2+1475c3e2+3496a2de2-13750abde2+2856b2de2-8745acde2-6751bcde2+
     ------------------------------------------------------------------------
     3167c2de2+8374ad2e2-10499bd2e2+13704cd2e2-2032d3e2+5013a2e3-1294abe3-
     ------------------------------------------------------------------------
     11353b2e3+332ace3+8412bce3+2157c2e3+9100ade3-14932bde3+11427cde3-65d2e3-
     ------------------------------------------------------------------------
     14085ae4-4294be4+7584ce4-1158de4+12691e5
     ------------------------------------------------------------------------
     a2c3+2932b2c3-10035ac4+5525bc4+15582c5-15381a2c2d+9112abc2d+14524b2c2d-
     ------------------------------------------------------------------------
     6332ac3d+6605bc3d+2396c4d-7789b3d2+13225a2cd2+7496abcd2+3650b2cd2+
     ------------------------------------------------------------------------
     5754ac2d2+6995bc2d2-14370c3d2-7801a2d3+6868abd3-11622b2d3+1521acd3+
     ------------------------------------------------------------------------
     8631bcd3-12932c2d3+6996ad4+1639bd4+15824cd4+5787d5-13041a2c2e-11514abc2e
     ------------------------------------------------------------------------
     +15900b2c2e+2487ac3e-2604bc3e+3846c4e+3798b3de-14196a2cde+10952abcde-
     ------------------------------------------------------------------------
     8536b2cde+1735ac2de-7812bc2de-12363c3de-1787a2d2e+10156abd2e+5682b2d2e+
     ------------------------------------------------------------------------
     1957acd2e+14005bcd2e+14459c2d2e+346ad3e-2891bd3e-5860cd3e-10602d4e-
     ------------------------------------------------------------------------
     1622b3e2+3059a2ce2+3613abce2-1406b2ce2+7442ac2e2+4275bc2e2+15318c3e2-
     ------------------------------------------------------------------------
     13078a2de2+4801abde2-1598b2de2-7884acde2+10369bcde2-7214c2de2-12919ad2e2
     ------------------------------------------------------------------------
     +9472bd2e2+7329cd2e2+2378d3e2-12471a2e3-13351abe3+9117b2e3+10490ace3+
     ------------------------------------------------------------------------
     12194bce3+2918c2e3+11909ade3-8687bde3+3578cde3-14970d2e3-11281ae4+
     ------------------------------------------------------------------------
     12593be4+15039ce4-13071de4-1082e5 |

             1       7
o6 : Matrix R  <--- R
i7 : leadTerm gbSnapshot(I)

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R